Method of Removing Noise In Seismic Reverse-Time Migration

ABSTRACT

A method, including: obtaining, with a processor, a seismic image of a subsurface region from a computer memory; predicting, with a processor, a dip of the seismic image of the subsurface region; and removing, with a processor, noise or artifacts from the seismic image of the subsurface region by applying a dip guided Laplacian filter, wherein the removing generates another seismic image of the subsurface region that has noise or artifacts removed relative to the seismic image of the subsurface region.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication 62/164,324 filed May 20, 2015 entitled METHOD OF REMOVINGNOISE IN SEISMIC REVERSE-TIME MIGRATION, the entirety of which isincorporated by reference herein.

FIELD OF THE INVENTION

The present technological advancement generally relates to the field ofgeophysical prospecting and, more particularly, a seismic image noisefiltering technique applied to images from wave-equation migration, suchas reverse-time migration.

BACKGROUND

This section is intended to introduce various aspects of the art, whichmay be associated with exemplary embodiments of the present invention.This discussion is believed to assist in providing a framework tofacilitate a better understanding of particular aspects of the presentinvention. Accordingly, it should be understood that this section shouldbe read in this light, and not necessarily as admissions of prior art.

Imaging techniques based on wave equations, such as Reverse-TimeMigration (RTM), have been widely applied to image the subsurface forhydrocarbon exploration. RTM is a very high fidelity imaging methodwhich is commonly applied in complex geology settings. It is also anexpensive algorithm. Furthermore, the traditional RTM image suffers fromlow-wavenumber noise created by backscattering energy from high-contrastboundaries in the models used by the imaging algorithm (Yoon et al.,2004; Fletcher et al., 2006; Sun et al., 2009; Douma et al., 2010).Various techniques have been tried to reduce and/or filter out thelow-wavenumber noise with some level of success. These techniques rangefrom modifications to the RTM imaging condition (Yoon et al., 2004;Douma et al., 2010), modification to the wave propagation equation toreduce the reflection from contrast boundaries in the imaging model(Fletcher et al., 2006), to the application of traditional Laplacianfilter to RTM raw images (Sun and Zhang, 2009).

Different techniques have different computational intensity requirementsand different effectiveness in removing the low-wavenumber noise.Techniques involving the application of different imaging conditions(Yoon et al., 2004; Douma et al., 2010) other than the direct zero-lagconvolution of source and receiver wave fields or the generation ofimage angle gathers tend to increase the computational costsubstantially.

Techniques in this category usually involve the calculation of wavepropagation direction, which is an expensive operation. Also, thecalculation of wave propagation direction in a complex geological areatends to have large error in the calculated wave propagation direction.This might cause leakage of the low-wavenumber noise in the image.

In practical applications, the traditional Laplacian filter technique(Sun and Zhang, 2009) is quite effective and computationally efficient.This is a post-imaging filter technique. There is no need to modify theimaging kernel, and thus the traditional efficient image condition ofdirect cross correlation of source and receiver wave field can be used.The filter is traditionally applied to the raw stacked image to filterout the low-wavenumber noise. Thus, it is computationally efficient.However, the traditional Laplacian filter operator is image dipindependent, or isotropic. The low-wavenumber noise and other coherentnoises from migration do show some directional characteristics. Despiteits high efficiency, it still cannot provide a satisfactory clean imageunder many situations.

SUMMARY

A method, including: obtaining, with a processor, a seismic image of asubsurface region from a computer memory; predicting, with a processor,a dip of the seismic image of the subsurface region; and removing, witha processor, noise or artifacts from the seismic image of the subsurfaceregion by applying a dip-guided Laplacian filter, wherein the removinggenerates another seismic image of the subsurface region that has noiseor artifacts removed relative to the seismic image of the subsurfaceregion.

In the method, the applying can include applying the dip-guidedLaplacian filter along a normal direction of the seismic image of thesubsurface region.

In the method, the obtaining can further include: dividing RTM inputseismic data by frequency squared; performing reverse-time migration byusing source and receiving wave field cross-correlation imagingcondition; and generating the seismic image of the subsurface region.

In the method, the removing can include using a mixed image-dip-guidedLaplacian filter, which includes a weighted combination of a Laplacianfilter and an image-dip-guided Laplacian filter.

In the method, the mixed image-dip-guided Laplacian filter can include anon-zero weighting parameter.

In the method, the weighting parameter can have a value in a range of0.1 to 0.5.

In the method, the weighting parameter can have a value greater thanzero and less than or equal to one.

In the method, the weighting parameter can be spatially dependent.

In the method, the weighting parameter can be only depth dependent.

In the method, the removing can include applying the mixed dip-guidedLaplacian filter multiple times, each with different values for theweighting parameter.

In the method, the predicting can include predicting image dip,partially or fully, by using a filtered image obtained in a previousiteration of the removing.

In the method, the predicting can include predicting the dip of theseismic image of the subsurface region from the seismic image of thesubsurface region or from prior dip knowledge in the subsurface region,or a combination of both.

BRIEF DESCRIPTION OF THE DRAWINGS

While the present disclosure is susceptible to various modifications andalternative forms, specific example embodiments thereof have been shownin the drawings and are herein described in detail. It should beunderstood, however, that the description herein of specific exampleembodiments is not intended to limit the disclosure to the particularforms disclosed herein, but on the contrary, this disclosure is to coverall modifications and equivalents as defined by the appended claims. Itshould also be understood that the drawings are not necessarily toscale, emphasis instead being placed upon clearly illustratingprinciples of exemplary embodiments of the present invention. Moreover,certain dimensions may be exaggerated to help visually convey suchprinciples.

FIG. 1A is a flow chart showing exemplary steps for removing noise fromseismic images from reverse-time migration.

FIG. 1B is a flow chart showing exemplary steps of predicting the imagedip by using the filtered image.

FIG. 2 is an example of seismic RTM raw stacked image and filteredimages: (a) raw stacked image before filter; (b) filtered image bytraditional Laplacian filter; (c) filtered image by the presenttechnological advancement with dip-guided weight α=0.3; and (d) filteredimage by the present technological advancement with dip-guided weightα=0.5.

FIG. 3 is an exemplary computer system useable with the presenttechnological advancement.

DETAILED DESCRIPTION

While the present disclosure is susceptible to various modifications andalternative forms, specific example embodiments thereof have been shownin the drawings and are herein described in detail. It should beunderstood, however, that the description herein of specific exampleembodiments is not intended to limit the disclosure to the particularforms disclosed herein, but on the contrary, this disclosure is to coverall modifications and equivalents as defined by the appended claims. Itshould also be understood that the drawings are not necessarily toscale, emphasis instead being placed upon clearly illustratingprinciples of exemplary embodiments of the present technologicaladvancement. Moreover, certain dimensions may be exaggerated to helpvisually convey such principles.

Exemplary methods described herein remove or filter noise from seismicimages obtained from a wave-equation imaging technique, such as RTM. Theexemplary methods described herein can provide an efficient and moreeffective post-imaging noise filtering technique than conventionaltechniques. A non-limiting embodiment of the present technologicaladvancement combines the efficient post-imaging filter technique andimage dip information to obtain a much cleaner filtered image. Forexample, such a non-limiting embodiment combines the efficientpost-imaging Laplacian-like filter with image dip information derivedeither from the image itself or from known geology dip information, suchas known horizons or geo-body boundaries, to achieve a more effectivenoise removing effect.

It is more effective to remove the noise by applying a Laplacian-likeoperator along the image normal direction. A Laplacian-like filteroperator along the image normal direction has been derived based on thepredicted dip information. Hereinafter, this filter is referred to as animage-dip-guided Laplacian filter. However, the present technologicaladvancement can be utilized while applying a Laplacian-like operatoralong other image directions.

To prevent the loss of weak signals, a mixed filter operator is designedto be the combination of the traditional Laplacian operator filter andthe image-dip-guided Laplacian filter derived below. A non-zero weightfactor is applied to the image-dip-guided Laplacian filter operator tocontrol the amount of contribution from it in the mixed filter operator.This mixed filter is hereinafter referred to as a mixed image-dip-guidedLaplacian filter.

Similar to the conventional Laplacian filter method, the input seismicdata to the imaging program should be pre-processed to integrate twicein time or divide by frequency square in the frequency domain tocompensate for the impact of the filter on the final image spectrum.

Use of the mixed image-dip-guided filter to remove noise from a raw RTMimage can obtain a better filtered RTM image and provide improvedcomputational efficiency of the image filter technique compared to othertechniques by either using modified RTM imaging conditions or modifiedwave propagation equations. As has been recognized previously,traditional RTM images suffer from low-wavenumber noise generated bybackscattering energy from high-contrast boundaries in the models usedby the imaging algorithm (Yoon et al., 2004; Fletcher et al., 2006; Sunet al., 2009; Douma et al., 2010). The traditional Laplacian filteroperator (Sun and Zhang, 2009) has worked reasonably well in removingthe low-wavenumber noise in some cases.

A conventional Laplacian filter operator applied to the RTM image,I(x,y,z), is given by,

$\begin{matrix}{{{\overset{\_}{I}\left( {x,y,z} \right)} = {{V^{2}\left( {x,y,z} \right)}\left( {\frac{\partial^{2}}{\partial^{2}x} + \frac{\partial^{2}}{\partial^{2}y} + \frac{\partial^{2}}{\partial^{2}z}} \right){I\left( {x,y,z} \right)}}},} & (1)\end{matrix}$

where V(x,y,z) is the imaging velocity, and (x,y,z) are the spatialCartesian coordinates in three-dimensional space, or (x,z) intwo-dimensional space, and Ī(x, y, z) is the filtered image. Thisconventional Laplacian filter operator is image dip independent, orisotropic. However, the low-wavenumber noise and other coherent noisesfrom migration do show some directional characteristics. Thisconventional Laplacian filter cannot provide a clean filtered image inlots of cases.

It has been determined that is more effective to remove the noise froman RTM image by applying a Laplacian-like operator along the imagenormal direction. In an exemplary embodiment of the presenttechnological advancement, instead of using the traditional filter inequation (1), the traditional Laplacian operator is replaced by an onedimensional Laplacian operator along the image dip direction as below,

$\begin{matrix}{{{\overset{\_}{I_{d\; g}}\left( {x,y,z} \right)} = {{V^{2}\left( {x,y,z} \right)}\frac{\partial^{2}{I\left( {x,y,z} \right)}}{\partial^{2}r_{k}}}},} & (2)\end{matrix}$

where

=r_(k)

, and

=[Kx, Ky, Kz], which is the unit vector along the local image normal dipdirection, and I_(dg) (x,y,z) is the image filtered by the dip-guidedLaplacian filter. After ignoring the spatial variation of the image dipand some algebra, the image-dip-guided Laplacian filter of eq. (2) isgiven by,

$\begin{matrix}{{\overset{\_}{I_{d\; g}}\left( {x,y,z} \right)} = {{V^{2}\left( {x,y,z} \right)}\left( {{K_{x}^{2}\frac{\partial^{2}}{\partial^{2}x}} + {K_{y}^{2}\frac{\partial^{2}}{\partial^{2}y}} + {K_{z}^{2}\frac{\partial^{2}}{\partial^{2}z}}} \right){{I\left( {x,y,z} \right)}.}}} & (3)\end{matrix}$

The image normal dip vector can be obtained by any dip estimationmethod, such as gradient structure tensor method and discrete scanmethod as discussed by Marfurt, (Marfurt, 2006). Mathematically, theunit dip normal vector can be predicted from the image as,

$\begin{matrix}{{\overset{\rightharpoonup}{K} = \frac{\nabla{I\left( {x,y,z} \right)}}{{\nabla{I\left( {x,y,z} \right)}}}},{and}} & (4) \\{{\nabla{I\left( {x,y,z} \right)}} = {\left\lbrack {\frac{\partial{I\left( {x,y,z} \right)}}{\partial x},\frac{\partial{I\left( {x,y,z} \right)}}{\partial y},\frac{\partial{I\left( {x,y,z} \right)}}{\partial z}} \right\rbrack.}} & (5)\end{matrix}$

The dip may also be predicted from the filtered image I_(dg) by usingeqs. (3), (4), and (5) in an iterative fashion. Optionally, the dipfield can be smoothed locally over space. The dip can also be obtainedfully or partially in space from prior geological knowledge about thesubsurface model if available, such as known horizons or geo-bodyboundaries in the image model. The image dip prediction from an imagecan also be based on the filtered image instead of the original rawimage, replacing the original image I in equations (4) and (5) byfiltered image I_(dg) or Ī. This makes the image filter an iterativeprocess.

The image-dip-guided Laplacian filter of equation (3) can not onlyenhance the effectiveness of the traditional low-wavenumber noisefiltering, but also enhance any stronger events in the image and reduceother weak events, such as weak migration swings. However, thisimage-dip-guided Laplacian filter could potentially filter out weaksignals if the predicted dip is not that of the signal that needs to bepreserved. To reduce this potential risk of filtering out a weak signaland to achieve a cleaner image, a mixed image-dip-guided Laplacianfilter can been designed by combining the traditional Laplacian filterof equation (1) and the image-dip-guided Laplacian filter of equation(3), which is given by

$\begin{matrix}{{\overset{\_}{I_{mix}}\left( {x,y,z} \right)} = {{V^{2}\left( {x,y,z} \right)}\left( {{w_{x}\frac{\partial^{2}}{\partial^{2}x}} + {w_{y}\frac{\partial^{2}}{\partial^{2}y}} + {w_{z}\frac{\partial^{2}}{\partial^{2}z}}} \right){{I\left( {x,y,z} \right)}.}}} & (6)\end{matrix}$

The three coefficients at front of the three second-order differentialoperators are given by

$\begin{matrix}{{{w_{x} = {{\alpha \; K_{x}^{2}} + \frac{1 - a}{3}}};}{{w_{y} = {{\alpha \; K_{y}^{2}} + \frac{1 - a}{3}}};}{{w_{z} = {{\alpha \; K_{z}^{2}} + \frac{1 - a}{3}}},}} & (7)\end{matrix}$

where [Kx, Ky, Kz] is the dip normal unit vector, a represents theweight of the dip-guided Laplacian filter of equation (3) in the mixedfilter of equation (6) and its value is between 0 and 1. The sum of thethree coefficients, w_(x), w_(y) , and w_(z), is automaticallynormalized to one, namely, w_(x)+w_(y)+w_(z)=K_(x) ²+K_(y) ²+K_(z) ²=1.

When α=1, we have w_(x)=K_(x) ², w_(y)=K_(y) ², w_(z)=K_(z) ². Equation(6) becomes the same as the full dip-guided Laplacian filter of equation(3).

When α=0, we have w_(x)=w_(y)=w_(z)=⅓. Equation (6) reduces to thetraditional full Laplacian filter of equation (1).

In general, the traditional full Laplacian filter, or α=0 in equations(6) and (7), does not bias any particular dip in filter operation due toits isotropic characteristics. It has less risk of filtering out anyparticular dipping event. However, the filtered image usually stillcontains undesired noise including the low-wavenumber noise and othermigration artifacts. The pure dip-guided filter, or α=1 in equations (6)and (7), can provide a much cleaner filtered image. However, it has anelevated risk of filtering out a weak but desired signal. The weightingparameter α can be adjusted to achieve the balance between the noiselevel left in the filtered image and the preservation of weak signal.

This mixed image-dip-guided Laplacian filter is computationallyefficient. One can apply this filter multiple times by using differentweighting parameter α and selecting the one which generates asatisfactory filtered image to user. Depending on the noise level andthe extent of existing crossing-dip (or conflicting dip, multiple eventsof different dips cross in space) events in the original image, one canadjust the weighting parameter α accordingly. The higher the noise level(both coherent and non-coherent) is, the lower the weighting parameter αshould be, and the higher the extent of existing crossing-dip events is,the lower the weighting parameter α should be in order to get an overallbetter filtered image with the preservation of weak and/or conflictingdip events. It has been found that α in the range of 0.1 to 0.5 tends togenerate satisfactory results in most practical applications.

In practical applications, α can also be spatial dependent to achieve anoptimal result in the whole image space. One simple example is to make αto be depth dependent only. In most cases, the low-wavenumber noiseexists above some high-contrast boundary in the imaging model. One canset α to a higher value in the depth range above the high-contrastboundary of strong noise, to a lower value in the depth range below thehigh-contrast boundary of a lower noise level, and make α changesmoothly from a value in one depth range to a value in another depthrange.

The filter operator shown by equations (6) and (7) is a second-orderdifferential operator with respect to space, which is similar to thetraditional Laplacian filter. The input seismic data to RTM should beprocessed by dividing the seismic data by frequency square in frequencydomain, or any other method which generate the same effect, tocompensate for the frequency spectra change caused by the Laplacianfilter. This will preserve the frequency spectrum of the final image.The factor of imaging velocity square in equation (6) is applied topreserve the image amplitude. This factor can be ignored if this imageamplitude compensation is not desired.

FIG. 1A illustrates an exemplary method of the present technologicaladvancement. Step 100 includes dividing the RTM input seismic data byfrequency square, or any other equivalent operation. Step 101 includesperforming RTM by using the traditional source and receiver wave fieldcross-correlation imaging condition and generating a raw stack image.Step 102 includes predicting the image dip; any prior knowledge aboutthe subsurface dip can be integrated in this dip prediction step. Theimage dip may also be predicted from the filtered image in an iterativeway. Step 103 includes selecting a dip-guided filter weight α. Step 104includes applying the mixed dip-guided Laplacian filter to the raw stackimage. Step 105 includes determining whether the filtered image issatisfactory; if yes, the filtering process is done; if not, the processreturns to step 103 to select another weighting factor value.

FIG. 1B illustrates an exemplary method of the present technologicaladvancement where predicting the image dip is accomplished by using thefiltered. Image. The steps in FIG. 1B are similar to those of FIG. 1A,except the process can go back to the image dip prediction step 102 fromstep 105 and use the filtered image from step 104 in the dip predictionof step 102.

FIG. 2 illustrates an example of the present technological advancementapplied to a seismic RTM raw stacked image. On the original raw stackedimage shown in FIG. 2 (a), the white cloud 200 at the center shallowpart is the so-called low-frequency noise. This type of noise exists atother parts of the image, but with much weaker amplitude. The filteredimage by traditional Laplacian filter is show in FIG. 2 (b). Thefiltered images by the method of the present technological advancementwith dip-guided weight α=0.3 and α=0.5 are shown in FIG. 2(c) and (d),respectively. Comparing image 2(d) to image 2(b), one can see that themethod of present technological advancement is more effective not onlyin removing the low-wavenumber noise (see noise inside the ellipses 201,202, and 203), but also in removing the very large dip weak migrationartifacts (nearly vertical weak events).

FIG. 3 is a block diagram of a computer system 2400 that can be used toexecute the present techniques. A central processing unit (CPU) 2402 iscoupled to system bus 2404. The CPU 2402 may be any general-purpose CPU,although other types of architectures of CPU 2402 (or other componentsof exemplary system 2400) may be used as long as CPU 2402 (and othercomponents of system 2400) supports the operations as described herein.Those of ordinary skill in the art will appreciate that, while only asingle CPU 2402 is shown in FIG. 3, additional CPUs may be present.Moreover, the computer system 2400 may comprise a networked,multi-processor computer system that may include a hybrid parallelCPU/GPU system. The CPU 2402 may execute the various logicalinstructions according to various teachings disclosed herein. Forexample, the CPU 2402 may execute machine-level instructions forperforming processing according to the operational flow described.

The computer system 2400 may also include computer components such asnontransitory, computer-readable media. Examples of computer-readablemedia include a random access memory (RAM) 2406, which may be SRAM,DRAM, SDRAM, or the like. The computer system 2400 may also includeadditional non-transitory, computer-readable media such as a read-onlymemory (ROM) 2408, which may be PROM, EPROM, EEPROM, or the like. RAM2406 and ROM 2408 hold user and system data and programs, as is known inthe art. The computer system 2400 may also include an input/output (I/O)adapter 2410, GPU(s) 2414, a communications adapter 2422, a userinterface adapter 2424, a display driver 2416, and a display adapter2418.

The I/O adapter 2410 may connect additional non-transitory,computer-readable media such as a storage device(s) 2412, including, forexample, a hard drive, a compact disc (CD) drive, a floppy disk drive, atape drive, and the like to computer system 2400. The storage device(s)may be used when RAM 2406 is insufficient for the memory requirementsassociated with storing data for operations of the present techniques.The data storage of the computer system 2400 may be used for storinginformation and/or other data used or generated as disclosed herein. Forexample, storage device(s) 2412 may be used to store configurationinformation or additional plug-ins in accordance with the presenttechniques. Further, user interface adapter 2424 couples user inputdevices, such as a keyboard 2428, a pointing device 2426 and/or outputdevices to the computer system 2400. The display adapter 2418 is drivenby the CPU 2402 to control the display on a display device 2420 to, forexample, present information to the user regarding available plug-ins.

The architecture of system 2400 may be varied as desired. For example,any suitable processor-based device may be used, including withoutlimitation personal computers, laptop computers, computer workstations,and multi-processor servers. Moreover, the present technologicaladvancement may be implemented on application specific integratedcircuits (ASICs) or very large scale integrated (VLSI) circuits. Infact, persons of ordinary skill in the art may use any number ofsuitable hardware structures capable of executing logical operationsaccording to the present technological advancement. The term “processingcircuit” encompasses a hardware processor (such as those found in thehardware devices noted above), ASICs, and VLSI circuits. Input data tothe computer system 2400 may include various plug-ins and library files.Input data may additionally include configuration information.

The foregoing description is directed to particular example embodimentsof the present technological advancement. It will be apparent, however,to one skilled in the art, that many modifications and variations to theembodiments described herein are possible. All such modifications andvariations are intended to be within the scope of the present invention,as defined in the appended claims. As will be obvious to the reader whoworks in the technical field, the present technological advancement isintended to be fully automated, or almost fully automated, using acomputer programmed in accordance with the disclosures herein.

The following references are hereby incorporated by reference in theirentirety:

Huub Douma, David Yingst, Ivan Vasconcelos, and Jeroen Tromp, “On theconnection between artifact filtering in reverse-time migration andadjoint tomography”, Geophysics Vol 75, NO. 6, P. S219-S223 (2010);

Robin P. Fletcher, Paul J. Fowler, Phil Kitchenside, and Uwe Albertin,“Suppressing unwanted internal reflections in prestack reverse-timemigration”, Geophysics Vol 71, NO. 6, P. E79-E82 (2006);

Kurt J. Marfurt, “Robust estimates of 3D reflector dip and azimuth”,Geophysics Vol 71, NO. 4, P P29-P40 (2006).

James Sun, Yu Zhang, “Practical issues of reverse time migration:true-amplitude gathers, noise removal and harmonic-source encoding”,ASEG Expanded Abstracts 2009 (Australian Society of ExplorationGeophysicists): 20^(th) Geophysical Conference; and

K. Yoon, K. Marfurt, and W. Starr, “Challenges in reverse-timemigration”: 74^(th) Annual International Meeting, SEG, ExpandedAbstracts, P. 1057-1060 (2004).

1. A method, comprising: obtaining, with a processor, a seismic image ofa subsurface region from a computer memory; predicting, with aprocessor, a dip of the seismic image of the subsurface region; andremoving, with a processor, noise or artifacts from the seismic image ofthe subsurface region by applying a dip-guided Laplacian filter, whereinthe removing generates another seismic image of the subsurface regionthat has noise or artifacts removed relative to the seismic image of thesubsurface region.
 2. The method of claim 1, wherein the applyingincludes applying the dip-guided Laplacian filter along a normaldirection of the seismic image of the subsurface region.
 3. The methodof claim 1, wherein the obtaining further comprises: dividing RTM inputseismic data by frequency squared; performing reverse-time migration byusing source and receiving wave field cross-correlation imagingcondition; and generating the seismic image of the subsurface region. 4.The method of claim 1, wherein the removing includes using a mixedimage-dip-guided Laplacian filter, which includes a weighted combinationof a Laplacian filter and an image-dip-guided Laplacian filter.
 5. Themethod of claim 4, wherein the mixed image-dip-guided Laplacian filterincludes a non-zero weighting parameter.
 6. The method of claim 5,wherein the weighting parameter has a value in a range of 0.1 to 0.5. 7.The method of claim 5, wherein the weighting parameter has value greaterthan zero and less than or equal to one.
 8. The method of claim 4,wherein the weighting parameter is spatially dependent.
 9. The method ofclaim 8, wherein the weighting parameter is only depth dependent. 10.The method of claim 4, wherein the removing includes applying the mixeddip-guided Laplacian filter multiple times, each with different valuesfor the weighting parameter.
 11. The method of claim 10, wherein thepredicting includes predicting image dip, partially or fully, by using afiltered image obtained in a previous iteration of the removing.
 12. Themethod of claim 1, wherein the predicting includes predicting the dip ofthe seismic image of the subsurface region from the seismic image of thesubsurface region or from prior dip knowledge in the subsurface region,or a combination of both.